Tony Blair has been criticised over his Middle East strategy
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Prime Minister Tony Blair believes there is "potential" for agreement on a UN resolution over the Middle East conflict in the next 24 hours.
Downing Street sources confirmed Mr Blair's views as Foreign Secretary Margaret Beckett described the situation in the region as "urgent".
She is cutting short her holiday to travel to the talks in New York.
More than 100 Labour MPs have demanded Parliament be recalled from its summer break to discuss the crisis.
The MPs have written to Deputy Prime Minister John Prescott saying the Commons should return "as soon as possible".
The prime minister spent the day talking to other world leaders on the phone as he continues his holiday in Barbados.
The timetable for an Israeli withdrawal from southern Lebanon is in dispute.
He is understood to have had a "productive" conversation with French President Jacques Chirac.
'Safe corridors'
Mr Blair has also spoken with UN Secretary General Kofi Annan where they both expressed optimism that a deal was close.
Meanwhile, Mrs Beckett said: "The situation is urgent and we need now to complete the task.
"The people of Lebanon and Israel are suffering. I am very concerned about the worsening humanitarian situation in the area."
She added: "We need to ensure that we make urgent progress in establishing safe corridors to move people and resources safely to where they are most needed in southern Lebanon."
In terms of the key discussions, France believes Israel should pull out as Lebanese troops take over, while the US supports a plan allowing Israeli forces to stay until an international force arrives.
'Disgrace'
On Thursday, the top humanitarian official at the UN said it was a "disgrace" that Israel and Hezbollah were denying aid agencies access to southern Lebanon.
Jan Egeland claimed it had been "many days" since relief workers had been allowed into an area in which hospitals were also running out of food and fuel.
The UN's World Food Programme has also demanded the two sides let through humanitarian aid.
More than 1,000 Lebanese, most of them civilians, have now died during a month of hostilities, according to the Lebanese government.
About 121 Israelis, most of them soldiers, have also been killed.